Inversion in a four-terminal superconducting device on the quartet line: I. Two-dimensional metal and the quartet beam splitter

Abstract

In connection with the recent Harvard group experiment on graphene-based four-terminal Josephson junctions containing a grounded loop, we consider biasing at opposite voltages on the quartet line and establish lowest-order perturbation theory in the tunnel amplitudes between a two-dimensional (2D) metal and four superconducting leads in the dirty limit. We present in addition general nonperturbative and nonadiabatic results. The critical current on the quartet line $I_c(\Phi /{\Phi }_0)$ depends on the reduced flux $\Phi /{\Phi }_0$ via interference between the three-terminal quartets (3TQ) and the nonstandard four-terminal split quartets (4TSQ). The 4TSQ result from synchronizing two Josephson junctions by exchange of two quasiparticles "surfing" on the 2D quantum wake, and this mechanism is already operational at equilibrium. Perturbation theory in the tunnel amplitudes shows that the 3TQ are $\pi$-shifted but the 4TSQ are $0$-shifted if the contacts have linear dimension which is large compared to the elastic mean free path. We establish the gate voltage dependence of the quartet critical current oscillations $I_c(\Phi /{\Phi }_0)$. It is argued that "Observation of $I_c(0)\ne I_c(1/2)$" implies "Evidence for the four-terminal 4TSQ" for finite bias voltage on the quartet line and arbitrary interface transparencies. This statement relies on physically-motivated approximations leading to the Ambegaokar-Baratoff-type formula for the quartet critical current-flux relation. It is concluded that the recent experiment mentioned above finds evidence for the four-terminal 4TSQ.

arXiv comment32 pages, 11 figures, supplemental material as ancillary file (7 pages, 2 figures). Minor corrections to the figures, Phys. Rev. B in press

References in corpus (29)

• Hamiltonian approach to the transport properties of superconducting quantum point contacts
• Correlated tunneling into a superconductor in a multiprobe hybrid structure
• Multi-terminal Josephson junctions as topological materials
• Photon assisted tunneling as an origin of the Dynes density of states
• Reversing non-local transport through a superconductor by electromagnetic excitations
• The $\omega$-SQUIPT: phase-engineering of Josephson topological materials
• Topological transconductance quantization in a four-terminal Josephson junction
• The multi-terminal Josephson effect
• Vanishing quasiparticle density in a hybrid Al/Cu/Al single-electron transistor
• Supercurrent Flow in Multi-Terminal Graphene Josephson Junctions
• Sign of the crossed conductances at a FSF double interface
• Production of non-local quartets and phase-sensitive entanglement in a superconducting beam splitter
• Nonlocal Josephson effect in Andreev molecules
• Non-local Supercurrent of Quartets in a Three-Terminal Josephson Junction
• Sub-Gap Structure in the Conductance of a Three-Terminal Josephson Junction
• Multipair DC-Josephson Resonances in a biased all-superconducting Bijunction
• Absence of split pairs in the cross-correlations of a highly transparent normal metal-superconductor-normal metal electron beam splitter
• Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction
• Engineering the Floquet spectrum of superconducting multiterminal quantum dots
• Berry phase in superconducting multiterminal quantum dots
• "Electro-flux" effect in superconducting hybrid Aharonov-Bohm rings
• Scattering description of Andreev molecules
• Contribution of weak localization to non local transport at normal metal / superconductor double interfaces
• Inversion in a four terminal superconducting device on the quartet line: II. Quantum dot and Floquet theory
• Gate-tunable zero-frequency current cross-correlations of the quartet mode in a voltage-biased three-terminal Josephson junction
• Partially resummed perturbation theory for multiple Andreev reflections in a short three-terminal Josephson junction
• Proposal for the observation of nonlocal multipair production: the biSQUID
• Quantum wakes in lattice fermions
• Phase-sensitive transport at a normal metal-superconductor interface close to a Josephson junction

Cited by in corpus (12)

• Inversion in a four terminal superconducting device on the quartet line: II. Quantum dot and Floquet theory
• A quantum interferometer for quartets in superconducting three-terminal Josephson junctions
• Ultralong-distance quantum correlations in three-terminal Josephson junctions
• Proposal for detecting the $\pi -$shifted Cooper quartet supercurrent
• Quartet Tomography in Multiterminal Josephson Junctions
• Magnetointerferometry of multiterminal Josephson junctions
• Nonlocal Josephson diode effect in minimal Kitaev chains
• Self-heating effects and switching dynamics in graphene multiterminal Josephson junctions
• Ballistic Andreev interferometers
• Nonequilibrium Andreev resonances in ballistic graphene Andreev interferometers
• Dynamical Stabilization of Multiplet Supercurrents in Multi-terminal Josephson Junctions
• Revisiting the adiabatic limit in ballistic multiterminal Josephson junctions